Tate Modern celebrates its fifth birthday this week. How wrong were the doomish prophets. People didn't just treat it like a mall for shopping and scoffing and getting out of the rain. The Turbine Hall wasn't just a children's playground.

Against all claims, visitors somehow managed to appreciate art that was not arranged according to chronology or movement. Great exhibitions were held and millions came back over and again as if to disprove the theory that the whole thing was no more than a gigantic novelty: many happy returns.

Over the years, however, there was a lingering question of how to present the very latest in contemporary art. Some of it appeared in huge theme shows like the ill-favoured Century City. Some of it, generally by the most established artists, appeared in solo shows - Luc Tuymans, Sigmar Polke - or was commissioned specially for the Unilever Series. One-off works were occasionally acquired and dotted through the 85 rooms of the museum. But even then, one had the sense of reputations already well burnished.

Risk-averse, you might say; that was the policy. But there is a space at Tate Modern, which opened last year, devoted to taking a chance. It is housed in a glass gallery outside the main building and it is scarcely heralded with a single signpost, let alone a fanfare on the map. Untitled, moreover, is its inauspicious title, as if harking back to the Seventies. But it promises the future (actually, it promises the Public World of the Private Space, but let that pass) and has so far housed some thorny, if adventurous shows.

The best is the current exhibition by young Mexican artist Damián Ortega. Ortega makes captivating installations out of everyday materials - a little city of shacks bearing strange histories in their scarred and rusting surfaces; another made of transparent plastic, fold-away and portable, the epitome of urban impermanence.

At Tate Modern, Ortega is showing all sorts of sculptures that refuse to behave like sculptures, that just won't sit there and be self-contained. Constructive Failure seems to be quite unfinished; three large and rickety open structures made of bits of wood tacked together that look set to falter at any moment.

Tangled in among them are three wooden chairs, hard to spot at first, but possibly the root of the problem, as if from their DNA this anomaly has grown.

Like an Escher staircase or a Piranesi prison, each strut seems to lead both up and down in continuum; hard to tell where things end or begin, if indeed they do. Ortega's sculpture seems to be still proliferating like an ever-expanding organism that knows no laws. Note his title, a play on that annoying oxymoron 'constructive criticism'.

Ortega was once a political cartoonist and the wit shows in much of his work: the elegant molecular structure made out of tortillas, fundamental food, one of which has disintegrated into chips on the floor. Or his elegant Running Gag, in which a chair seems to collapse backwards in stages, like the successive frames of a cartoon, while remaining one continuous sculpture, defiant of time and winking cheerfully at Duchamp's (merely 2D) Nude Descending a Staircase

But there are grave undertones among the wryness, particularly in a strangely beautiful sculpture in which the panes of a window appear to have shattered outwards at different velocities from their frame, but are held suspended in midair. The first is slightly cracked, the second more splintered and so on until the very last, and furthermost, pane in which the damage is so great that the glass is almost milky with fractures. Yet you can still see through it, just, to what went before: how violence leads only backwards, and, of course, forwards to violence.

Untitled is the way forward and may it expand accordingly when Tate Modern doubles in size. But Tate Britain has long had a dedicated gallery for these brief glimpses of the young, the promising and the newly up-and-come, namely Art Now, housed in the remotest corner of the building.

Opening this week, Scottish artist Andrew Grassie has made an exhibition of the space itself. Or, rather, an exhibition of an exhibition that might, or might not, have existed in that gallery, a wistfully virtual show of some of the artists he most admires.

Over several months, Grassie chose works from the Tate Collection - Turner, Picasso, Stubbs, Bridget Riley - and had them briefly brought to the Art Now gallery. Here, they would be hung, perhaps two at a time, and he would photograph the display and assemble the fragmentary record so that it appeared to represent a real, if wonderfully implausible, show.

Whereupon - most extreme of all - the artist then painted copies of the photographs in tempera with such exquisite accuracy that they completely deceive the eye.

Now this may sound like an otiose exercise in self-referentiality, but that is not at all how it feels. To begin with, there is something very disorienting about Grassie's images. Stand before each of the 13 paintings and you are looking at the very spot where you stand, confronted by a representation of a painting that is no longer here.

Further, Grassie's paintings always show the gallery at odd angles. So you walk up to them expecting a straight simulacrum of the wall you're approaching, but find, instead, the viewpoint strangely skewed, as if you were arriving from round a corner. Sometimes, you can't quite identify the painting within the painting because you only see the distant edge of a frame, exactly the experience of negotiating a crowded gallery.

Odder still is the way that Grassie has completely neutralised the fact that his images are paintings at all; so deceptive, so flawless, they go beyond photorealism altogether. Yet they do have a peculiarly lambent quality that takes them far beyond the camera.

It's an elusiveness consistent with the diffident melancholy of the whole installation - unreal records of an event that never quite took place, only a virtual joy; homages by a painter who hardly wishes to draw attention to his own - as opposed to other people's - paintings.